Splitting multidimensional necklaces

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dc.creatorde Longueville, Mark
dc.creatorZivaljevic, Rade
dc.date2006-10-26
dc.date.accessioned2026-07-07T07:29:28Z
dc.date.available2026-07-07T07:29:28Z
dc.descriptionThe well-known "splitting necklace theorem" of Noga Alon says that each "necklace" having beads of n different colors can be fairly divided between k "thieves" by at most n(k-1) cuts. We demonstrate that Alon's result is a special case of a multidimensional, consensus division theorem for n continuous probability measures on a d-cube [0,1]^d. The dissection is performed by m_1+...+ m_d=n(k-1) hyperplanes parallel to the sides of [0,1]^d dividing the cube into m_1 x m_2 x ... x m_d elementary parallelepipeds where the integers m_i are prescribed in advance.
dc.identifierhttps://arxiv.org/abs/math/0610800
dc.identifierhttp://arxiv.org/abs/math/0610800
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118125
dc.subjectCombinatorics
dc.subjectAlgebraic Topology
dc.subject05C10; 51M16, 52A40, 52B22, 55N91
dc.titleSplitting multidimensional necklaces
dc.typetext

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